Velocity distribution and hydrodynamic drag in turbulent flow

Abstract

This work aims to study the vertical velocity distribution in the near-wall layer of a pipe, channel, and boundary layer of a flat plate because these issues are of great practical and theoretical importance. Until now, engineering calculations of turbulent flows have been based on empirical formulas derived in the last century. The theory of turbulent fluid motion has not been completed, and the issues of velocity distribution and hydraulic resistance remain open for further study. It is known that velocity distribution in the flow is intricately linked to hydraulic resistance. Therefore, the study’s objectives also include determining the position of the point of maximum turbulent tangential stresses and comparing the change in tangential stresses with the logarithmic velocity profile. Based on calculation and analytical methods, we have researched the distribution of the turbulent component of the tangential stress along the depth of the flow. Derived an expression determining the position of the maximum point of the turbulent component of the tangential stress for smooth tubes. The contribution of the viscous component of the tangential stress at different points along the flow depth has been evaluated. The calculation results determining the position of the maximum point of the turbulent component of the tangential stress were compared with experimental data on velocity distribution in the flow. With the decrease of the hydraulic resistance coefficient, the point of maximum turbulent tangential stresses shifts towards the solid flow boundary. Based on the results of comparing the maximum turbulent tangential stresses with the total tangential stress, we can conclude that the contribution of the viscous component of the tangential stress to the total amount of friction and its influence on velocity distribution is significant. The angular coefficient of the velocity profile for the flow core is determined.